where \(J_\nu (z), Y_\nu (z)\)  are Bessel functions of the first and second kind, respectively [1]}. Moreover, Entry 2.19.4.13 in [2]}, Vol. II represents the product \(x^n \rho _\nu (x)\)  in terms of the associated Laguerre polynomials [3]}. Precisely, it has
\({(-1)^n x^n\over n!}\ \rho _\nu (x)= \int _0^\infty y^{\nu +n -1} e^{-y - x/y} L_n^\nu (y) dy,\quad n \in \mathbb {N}_{0}.\qquad \mathrm {(1.10)}\) 
